计算下列各极限lim x^2+2x-2x->-1 ---------x^2+1 limx->无穷 (1+1/x)(2-1/x^2)limx->-1 (x^2+2x-2)/(x^2+1)
问题描述:
计算下列各极限
lim x^2+2x-2
x->-1 ---------
x^2+1
lim
x->无穷 (1+1/x)(2-1/x^2)
lim
x->-1 (x^2+2x-2)/(x^2+1)
答
1.lim(x^2+2x -2)/(x^2+1)=
只要把x=-1代人上面式子即可
所以:lim(x^2+2x -2)/(x^2+1)=(1-2-2)/(1+1)=-3/2
2.lim
x->无穷 (1+1/x)(2-1/x^2)
当x趋向∞时,1/x趋向0.1/x^2趋向0
所以:lim
x->无穷 (1+1/x)(2-1/x^2)=(1+0)(2-0)=2